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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.analysis.polynomials;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math.DuplicateSampleAbscissaException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.exception.util.LocalizedFormats;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math.util.FastMath;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Implements the representation of a real polynomial function in<a name="line.27"></a>
<FONT color="green">028</FONT>     * &lt;a href="http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html"&gt;<a name="line.28"></a>
<FONT color="green">029</FONT>     * Lagrange Form&lt;/a&gt;. For reference, see &lt;b&gt;Introduction to Numerical<a name="line.29"></a>
<FONT color="green">030</FONT>     * Analysis&lt;/b&gt;, ISBN 038795452X, chapter 2.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * The approximated function should be smooth enough for Lagrange polynomial<a name="line.32"></a>
<FONT color="green">033</FONT>     * to work well. Otherwise, consider using splines instead.&lt;/p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 f??vr. 2011) $<a name="line.35"></a>
<FONT color="green">036</FONT>     * @since 1.2<a name="line.36"></a>
<FONT color="green">037</FONT>     */<a name="line.37"></a>
<FONT color="green">038</FONT>    public class PolynomialFunctionLagrangeForm implements UnivariateRealFunction {<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /**<a name="line.40"></a>
<FONT color="green">041</FONT>         * The coefficients of the polynomial, ordered by degree -- i.e.<a name="line.41"></a>
<FONT color="green">042</FONT>         * coefficients[0] is the constant term and coefficients[n] is the<a name="line.42"></a>
<FONT color="green">043</FONT>         * coefficient of x^n where n is the degree of the polynomial.<a name="line.43"></a>
<FONT color="green">044</FONT>         */<a name="line.44"></a>
<FONT color="green">045</FONT>        private double coefficients[];<a name="line.45"></a>
<FONT color="green">046</FONT>    <a name="line.46"></a>
<FONT color="green">047</FONT>        /**<a name="line.47"></a>
<FONT color="green">048</FONT>         * Interpolating points (abscissas).<a name="line.48"></a>
<FONT color="green">049</FONT>         */<a name="line.49"></a>
<FONT color="green">050</FONT>        private final double x[];<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>        /**<a name="line.52"></a>
<FONT color="green">053</FONT>         * Function values at interpolating points.<a name="line.53"></a>
<FONT color="green">054</FONT>         */<a name="line.54"></a>
<FONT color="green">055</FONT>        private final double y[];<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>        /**<a name="line.57"></a>
<FONT color="green">058</FONT>         * Whether the polynomial coefficients are available.<a name="line.58"></a>
<FONT color="green">059</FONT>         */<a name="line.59"></a>
<FONT color="green">060</FONT>        private boolean coefficientsComputed;<a name="line.60"></a>
<FONT color="green">061</FONT>    <a name="line.61"></a>
<FONT color="green">062</FONT>        /**<a name="line.62"></a>
<FONT color="green">063</FONT>         * Construct a Lagrange polynomial with the given abscissas and function<a name="line.63"></a>
<FONT color="green">064</FONT>         * values. The order of interpolating points are not important.<a name="line.64"></a>
<FONT color="green">065</FONT>         * &lt;p&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>         * The constructor makes copy of the input arrays and assigns them.&lt;/p&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         *<a name="line.67"></a>
<FONT color="green">068</FONT>         * @param x interpolating points<a name="line.68"></a>
<FONT color="green">069</FONT>         * @param y function values at interpolating points<a name="line.69"></a>
<FONT color="green">070</FONT>         * @throws IllegalArgumentException if input arrays are not valid<a name="line.70"></a>
<FONT color="green">071</FONT>         */<a name="line.71"></a>
<FONT color="green">072</FONT>        public PolynomialFunctionLagrangeForm(double x[], double y[])<a name="line.72"></a>
<FONT color="green">073</FONT>            throws IllegalArgumentException {<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>            verifyInterpolationArray(x, y);<a name="line.75"></a>
<FONT color="green">076</FONT>            this.x = new double[x.length];<a name="line.76"></a>
<FONT color="green">077</FONT>            this.y = new double[y.length];<a name="line.77"></a>
<FONT color="green">078</FONT>            System.arraycopy(x, 0, this.x, 0, x.length);<a name="line.78"></a>
<FONT color="green">079</FONT>            System.arraycopy(y, 0, this.y, 0, y.length);<a name="line.79"></a>
<FONT color="green">080</FONT>            coefficientsComputed = false;<a name="line.80"></a>
<FONT color="green">081</FONT>        }<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /** {@inheritDoc} */<a name="line.83"></a>
<FONT color="green">084</FONT>        public double value(double z) throws FunctionEvaluationException {<a name="line.84"></a>
<FONT color="green">085</FONT>            try {<a name="line.85"></a>
<FONT color="green">086</FONT>                return evaluate(x, y, z);<a name="line.86"></a>
<FONT color="green">087</FONT>            } catch (DuplicateSampleAbscissaException e) {<a name="line.87"></a>
<FONT color="green">088</FONT>                throw new FunctionEvaluationException(z, e.getSpecificPattern(), e.getGeneralPattern(), e.getArguments());<a name="line.88"></a>
<FONT color="green">089</FONT>            }<a name="line.89"></a>
<FONT color="green">090</FONT>        }<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>        /**<a name="line.92"></a>
<FONT color="green">093</FONT>         * Returns the degree of the polynomial.<a name="line.93"></a>
<FONT color="green">094</FONT>         *<a name="line.94"></a>
<FONT color="green">095</FONT>         * @return the degree of the polynomial<a name="line.95"></a>
<FONT color="green">096</FONT>         */<a name="line.96"></a>
<FONT color="green">097</FONT>        public int degree() {<a name="line.97"></a>
<FONT color="green">098</FONT>            return x.length - 1;<a name="line.98"></a>
<FONT color="green">099</FONT>        }<a name="line.99"></a>
<FONT color="green">100</FONT>    <a name="line.100"></a>
<FONT color="green">101</FONT>        /**<a name="line.101"></a>
<FONT color="green">102</FONT>         * Returns a copy of the interpolating points array.<a name="line.102"></a>
<FONT color="green">103</FONT>         * &lt;p&gt;<a name="line.103"></a>
<FONT color="green">104</FONT>         * Changes made to the returned copy will not affect the polynomial.&lt;/p&gt;<a name="line.104"></a>
<FONT color="green">105</FONT>         *<a name="line.105"></a>
<FONT color="green">106</FONT>         * @return a fresh copy of the interpolating points array<a name="line.106"></a>
<FONT color="green">107</FONT>         */<a name="line.107"></a>
<FONT color="green">108</FONT>        public double[] getInterpolatingPoints() {<a name="line.108"></a>
<FONT color="green">109</FONT>            double[] out = new double[x.length];<a name="line.109"></a>
<FONT color="green">110</FONT>            System.arraycopy(x, 0, out, 0, x.length);<a name="line.110"></a>
<FONT color="green">111</FONT>            return out;<a name="line.111"></a>
<FONT color="green">112</FONT>        }<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>        /**<a name="line.114"></a>
<FONT color="green">115</FONT>         * Returns a copy of the interpolating values array.<a name="line.115"></a>
<FONT color="green">116</FONT>         * &lt;p&gt;<a name="line.116"></a>
<FONT color="green">117</FONT>         * Changes made to the returned copy will not affect the polynomial.&lt;/p&gt;<a name="line.117"></a>
<FONT color="green">118</FONT>         *<a name="line.118"></a>
<FONT color="green">119</FONT>         * @return a fresh copy of the interpolating values array<a name="line.119"></a>
<FONT color="green">120</FONT>         */<a name="line.120"></a>
<FONT color="green">121</FONT>        public double[] getInterpolatingValues() {<a name="line.121"></a>
<FONT color="green">122</FONT>            double[] out = new double[y.length];<a name="line.122"></a>
<FONT color="green">123</FONT>            System.arraycopy(y, 0, out, 0, y.length);<a name="line.123"></a>
<FONT color="green">124</FONT>            return out;<a name="line.124"></a>
<FONT color="green">125</FONT>        }<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>        /**<a name="line.127"></a>
<FONT color="green">128</FONT>         * Returns a copy of the coefficients array.<a name="line.128"></a>
<FONT color="green">129</FONT>         * &lt;p&gt;<a name="line.129"></a>
<FONT color="green">130</FONT>         * Changes made to the returned copy will not affect the polynomial.&lt;/p&gt;<a name="line.130"></a>
<FONT color="green">131</FONT>         * &lt;p&gt;<a name="line.131"></a>
<FONT color="green">132</FONT>         * Note that coefficients computation can be ill-conditioned. Use with caution<a name="line.132"></a>
<FONT color="green">133</FONT>         * and only when it is necessary.&lt;/p&gt;<a name="line.133"></a>
<FONT color="green">134</FONT>         *<a name="line.134"></a>
<FONT color="green">135</FONT>         * @return a fresh copy of the coefficients array<a name="line.135"></a>
<FONT color="green">136</FONT>         */<a name="line.136"></a>
<FONT color="green">137</FONT>        public double[] getCoefficients() {<a name="line.137"></a>
<FONT color="green">138</FONT>            if (!coefficientsComputed) {<a name="line.138"></a>
<FONT color="green">139</FONT>                computeCoefficients();<a name="line.139"></a>
<FONT color="green">140</FONT>            }<a name="line.140"></a>
<FONT color="green">141</FONT>            double[] out = new double[coefficients.length];<a name="line.141"></a>
<FONT color="green">142</FONT>            System.arraycopy(coefficients, 0, out, 0, coefficients.length);<a name="line.142"></a>
<FONT color="green">143</FONT>            return out;<a name="line.143"></a>
<FONT color="green">144</FONT>        }<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>        /**<a name="line.146"></a>
<FONT color="green">147</FONT>         * Evaluate the Lagrange polynomial using<a name="line.147"></a>
<FONT color="green">148</FONT>         * &lt;a href="http://mathworld.wolfram.com/NevillesAlgorithm.html"&gt;<a name="line.148"></a>
<FONT color="green">149</FONT>         * Neville's Algorithm&lt;/a&gt;. It takes O(N^2) time.<a name="line.149"></a>
<FONT color="green">150</FONT>         * &lt;p&gt;<a name="line.150"></a>
<FONT color="green">151</FONT>         * This function is made public static so that users can call it directly<a name="line.151"></a>
<FONT color="green">152</FONT>         * without instantiating PolynomialFunctionLagrangeForm object.&lt;/p&gt;<a name="line.152"></a>
<FONT color="green">153</FONT>         *<a name="line.153"></a>
<FONT color="green">154</FONT>         * @param x the interpolating points array<a name="line.154"></a>
<FONT color="green">155</FONT>         * @param y the interpolating values array<a name="line.155"></a>
<FONT color="green">156</FONT>         * @param z the point at which the function value is to be computed<a name="line.156"></a>
<FONT color="green">157</FONT>         * @return the function value<a name="line.157"></a>
<FONT color="green">158</FONT>         * @throws DuplicateSampleAbscissaException if the sample has duplicate abscissas<a name="line.158"></a>
<FONT color="green">159</FONT>         * @throws IllegalArgumentException if inputs are not valid<a name="line.159"></a>
<FONT color="green">160</FONT>         */<a name="line.160"></a>
<FONT color="green">161</FONT>        public static double evaluate(double x[], double y[], double z) throws<a name="line.161"></a>
<FONT color="green">162</FONT>            DuplicateSampleAbscissaException, IllegalArgumentException {<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>            verifyInterpolationArray(x, y);<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>            int nearest = 0;<a name="line.166"></a>
<FONT color="green">167</FONT>            final int n = x.length;<a name="line.167"></a>
<FONT color="green">168</FONT>            final double[] c = new double[n];<a name="line.168"></a>
<FONT color="green">169</FONT>            final double[] d = new double[n];<a name="line.169"></a>
<FONT color="green">170</FONT>            double min_dist = Double.POSITIVE_INFINITY;<a name="line.170"></a>
<FONT color="green">171</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.171"></a>
<FONT color="green">172</FONT>                // initialize the difference arrays<a name="line.172"></a>
<FONT color="green">173</FONT>                c[i] = y[i];<a name="line.173"></a>
<FONT color="green">174</FONT>                d[i] = y[i];<a name="line.174"></a>
<FONT color="green">175</FONT>                // find out the abscissa closest to z<a name="line.175"></a>
<FONT color="green">176</FONT>                final double dist = FastMath.abs(z - x[i]);<a name="line.176"></a>
<FONT color="green">177</FONT>                if (dist &lt; min_dist) {<a name="line.177"></a>
<FONT color="green">178</FONT>                    nearest = i;<a name="line.178"></a>
<FONT color="green">179</FONT>                    min_dist = dist;<a name="line.179"></a>
<FONT color="green">180</FONT>                }<a name="line.180"></a>
<FONT color="green">181</FONT>            }<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>            // initial approximation to the function value at z<a name="line.183"></a>
<FONT color="green">184</FONT>            double value = y[nearest];<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>            for (int i = 1; i &lt; n; i++) {<a name="line.186"></a>
<FONT color="green">187</FONT>                for (int j = 0; j &lt; n-i; j++) {<a name="line.187"></a>
<FONT color="green">188</FONT>                    final double tc = x[j] - z;<a name="line.188"></a>
<FONT color="green">189</FONT>                    final double td = x[i+j] - z;<a name="line.189"></a>
<FONT color="green">190</FONT>                    final double divider = x[j] - x[i+j];<a name="line.190"></a>
<FONT color="green">191</FONT>                    if (divider == 0.0) {<a name="line.191"></a>
<FONT color="green">192</FONT>                        // This happens only when two abscissas are identical.<a name="line.192"></a>
<FONT color="green">193</FONT>                        throw new DuplicateSampleAbscissaException(x[i], i, i+j);<a name="line.193"></a>
<FONT color="green">194</FONT>                    }<a name="line.194"></a>
<FONT color="green">195</FONT>                    // update the difference arrays<a name="line.195"></a>
<FONT color="green">196</FONT>                    final double w = (c[j+1] - d[j]) / divider;<a name="line.196"></a>
<FONT color="green">197</FONT>                    c[j] = tc * w;<a name="line.197"></a>
<FONT color="green">198</FONT>                    d[j] = td * w;<a name="line.198"></a>
<FONT color="green">199</FONT>                }<a name="line.199"></a>
<FONT color="green">200</FONT>                // sum up the difference terms to get the final value<a name="line.200"></a>
<FONT color="green">201</FONT>                if (nearest &lt; 0.5*(n-i+1)) {<a name="line.201"></a>
<FONT color="green">202</FONT>                    value += c[nearest];    // fork down<a name="line.202"></a>
<FONT color="green">203</FONT>                } else {<a name="line.203"></a>
<FONT color="green">204</FONT>                    nearest--;<a name="line.204"></a>
<FONT color="green">205</FONT>                    value += d[nearest];    // fork up<a name="line.205"></a>
<FONT color="green">206</FONT>                }<a name="line.206"></a>
<FONT color="green">207</FONT>            }<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>            return value;<a name="line.209"></a>
<FONT color="green">210</FONT>        }<a name="line.210"></a>
<FONT color="green">211</FONT>    <a name="line.211"></a>
<FONT color="green">212</FONT>        /**<a name="line.212"></a>
<FONT color="green">213</FONT>         * Calculate the coefficients of Lagrange polynomial from the<a name="line.213"></a>
<FONT color="green">214</FONT>         * interpolation data. It takes O(N^2) time.<a name="line.214"></a>
<FONT color="green">215</FONT>         * &lt;p&gt;<a name="line.215"></a>
<FONT color="green">216</FONT>         * Note this computation can be ill-conditioned. Use with caution<a name="line.216"></a>
<FONT color="green">217</FONT>         * and only when it is necessary.&lt;/p&gt;<a name="line.217"></a>
<FONT color="green">218</FONT>         *<a name="line.218"></a>
<FONT color="green">219</FONT>         * @throws ArithmeticException if any abscissas coincide<a name="line.219"></a>
<FONT color="green">220</FONT>         */<a name="line.220"></a>
<FONT color="green">221</FONT>        protected void computeCoefficients() throws ArithmeticException {<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>            final int n = degree() + 1;<a name="line.223"></a>
<FONT color="green">224</FONT>            coefficients = new double[n];<a name="line.224"></a>
<FONT color="green">225</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.225"></a>
<FONT color="green">226</FONT>                coefficients[i] = 0.0;<a name="line.226"></a>
<FONT color="green">227</FONT>            }<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>            // c[] are the coefficients of P(x) = (x-x[0])(x-x[1])...(x-x[n-1])<a name="line.229"></a>
<FONT color="green">230</FONT>            final double[] c = new double[n+1];<a name="line.230"></a>
<FONT color="green">231</FONT>            c[0] = 1.0;<a name="line.231"></a>
<FONT color="green">232</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.232"></a>
<FONT color="green">233</FONT>                for (int j = i; j &gt; 0; j--) {<a name="line.233"></a>
<FONT color="green">234</FONT>                    c[j] = c[j-1] - c[j] * x[i];<a name="line.234"></a>
<FONT color="green">235</FONT>                }<a name="line.235"></a>
<FONT color="green">236</FONT>                c[0] *= -x[i];<a name="line.236"></a>
<FONT color="green">237</FONT>                c[i+1] = 1;<a name="line.237"></a>
<FONT color="green">238</FONT>            }<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>            final double[] tc = new double[n];<a name="line.240"></a>
<FONT color="green">241</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.241"></a>
<FONT color="green">242</FONT>                // d = (x[i]-x[0])...(x[i]-x[i-1])(x[i]-x[i+1])...(x[i]-x[n-1])<a name="line.242"></a>
<FONT color="green">243</FONT>                double d = 1;<a name="line.243"></a>
<FONT color="green">244</FONT>                for (int j = 0; j &lt; n; j++) {<a name="line.244"></a>
<FONT color="green">245</FONT>                    if (i != j) {<a name="line.245"></a>
<FONT color="green">246</FONT>                        d *= x[i] - x[j];<a name="line.246"></a>
<FONT color="green">247</FONT>                    }<a name="line.247"></a>
<FONT color="green">248</FONT>                }<a name="line.248"></a>
<FONT color="green">249</FONT>                if (d == 0.0) {<a name="line.249"></a>
<FONT color="green">250</FONT>                    // This happens only when two abscissas are identical.<a name="line.250"></a>
<FONT color="green">251</FONT>                    for (int k = 0; k &lt; n; ++k) {<a name="line.251"></a>
<FONT color="green">252</FONT>                        if ((i != k) &amp;&amp; (x[i] == x[k])) {<a name="line.252"></a>
<FONT color="green">253</FONT>                            throw MathRuntimeException.createArithmeticException(<a name="line.253"></a>
<FONT color="green">254</FONT>                                  LocalizedFormats.IDENTICAL_ABSCISSAS_DIVISION_BY_ZERO,<a name="line.254"></a>
<FONT color="green">255</FONT>                                  i, k, x[i]);<a name="line.255"></a>
<FONT color="green">256</FONT>                        }<a name="line.256"></a>
<FONT color="green">257</FONT>                    }<a name="line.257"></a>
<FONT color="green">258</FONT>                }<a name="line.258"></a>
<FONT color="green">259</FONT>                final double t = y[i] / d;<a name="line.259"></a>
<FONT color="green">260</FONT>                // Lagrange polynomial is the sum of n terms, each of which is a<a name="line.260"></a>
<FONT color="green">261</FONT>                // polynomial of degree n-1. tc[] are the coefficients of the i-th<a name="line.261"></a>
<FONT color="green">262</FONT>                // numerator Pi(x) = (x-x[0])...(x-x[i-1])(x-x[i+1])...(x-x[n-1]).<a name="line.262"></a>
<FONT color="green">263</FONT>                tc[n-1] = c[n];     // actually c[n] = 1<a name="line.263"></a>
<FONT color="green">264</FONT>                coefficients[n-1] += t * tc[n-1];<a name="line.264"></a>
<FONT color="green">265</FONT>                for (int j = n-2; j &gt;= 0; j--) {<a name="line.265"></a>
<FONT color="green">266</FONT>                    tc[j] = c[j+1] + tc[j+1] * x[i];<a name="line.266"></a>
<FONT color="green">267</FONT>                    coefficients[j] += t * tc[j];<a name="line.267"></a>
<FONT color="green">268</FONT>                }<a name="line.268"></a>
<FONT color="green">269</FONT>            }<a name="line.269"></a>
<FONT color="green">270</FONT>    <a name="line.270"></a>
<FONT color="green">271</FONT>            coefficientsComputed = true;<a name="line.271"></a>
<FONT color="green">272</FONT>        }<a name="line.272"></a>
<FONT color="green">273</FONT>    <a name="line.273"></a>
<FONT color="green">274</FONT>        /**<a name="line.274"></a>
<FONT color="green">275</FONT>         * Verifies that the interpolation arrays are valid.<a name="line.275"></a>
<FONT color="green">276</FONT>         * &lt;p&gt;<a name="line.276"></a>
<FONT color="green">277</FONT>         * The arrays features checked by this method are that both arrays have the<a name="line.277"></a>
<FONT color="green">278</FONT>         * same length and this length is at least 2.<a name="line.278"></a>
<FONT color="green">279</FONT>         * &lt;/p&gt;<a name="line.279"></a>
<FONT color="green">280</FONT>         * &lt;p&gt;<a name="line.280"></a>
<FONT color="green">281</FONT>         * The interpolating points must be distinct. However it is not<a name="line.281"></a>
<FONT color="green">282</FONT>         * verified here, it is checked in evaluate() and computeCoefficients().<a name="line.282"></a>
<FONT color="green">283</FONT>         * &lt;/p&gt;<a name="line.283"></a>
<FONT color="green">284</FONT>         *<a name="line.284"></a>
<FONT color="green">285</FONT>         * @param x the interpolating points array<a name="line.285"></a>
<FONT color="green">286</FONT>         * @param y the interpolating values array<a name="line.286"></a>
<FONT color="green">287</FONT>         * @throws IllegalArgumentException if not valid<a name="line.287"></a>
<FONT color="green">288</FONT>         * @see #evaluate(double[], double[], double)<a name="line.288"></a>
<FONT color="green">289</FONT>         * @see #computeCoefficients()<a name="line.289"></a>
<FONT color="green">290</FONT>         */<a name="line.290"></a>
<FONT color="green">291</FONT>        public static void verifyInterpolationArray(double x[], double y[])<a name="line.291"></a>
<FONT color="green">292</FONT>            throws IllegalArgumentException {<a name="line.292"></a>
<FONT color="green">293</FONT>    <a name="line.293"></a>
<FONT color="green">294</FONT>            if (x.length != y.length) {<a name="line.294"></a>
<FONT color="green">295</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.295"></a>
<FONT color="green">296</FONT>                      LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, x.length, y.length);<a name="line.296"></a>
<FONT color="green">297</FONT>            }<a name="line.297"></a>
<FONT color="green">298</FONT>    <a name="line.298"></a>
<FONT color="green">299</FONT>            if (x.length &lt; 2) {<a name="line.299"></a>
<FONT color="green">300</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.300"></a>
<FONT color="green">301</FONT>                      LocalizedFormats.WRONG_NUMBER_OF_POINTS, 2, x.length);<a name="line.301"></a>
<FONT color="green">302</FONT>            }<a name="line.302"></a>
<FONT color="green">303</FONT>    <a name="line.303"></a>
<FONT color="green">304</FONT>        }<a name="line.304"></a>
<FONT color="green">305</FONT>    }<a name="line.305"></a>




























































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